Load balancing is a critical factor in achieving optimal performance in parallel applications where tasks are created in a dynamic fashion. In many computations, such as state space search problems, tasks have priorities, and solutions to the computation may be achieved more efficiently if these priorities are adhered to in the parallel execution of the tasks. For such tasks, a load balancing scheme that only seeks to balance load, without balancing high priority tasks over the entire system, might result in the concentration of high priority tasks (even in a balanced-load environment) on a few processors, thereby leading to low priority work being done. In such situations a load balancing scheme is desired which would balance both load and high priority tasks over the system. The authors describe the development of a more efficient prioritized load balancing strategy.